### Parity Systems and the Delta-Matroid Intersection Problem

André Bouchet, Bill Jackson
<span title="1999-09-03">1999</span> <i title="The Electronic Journal of Combinatorics"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/v5dyak6ulffqfara7hmuchh24a" style="color: black;">Electronic Journal of Combinatorics</a> </i> &nbsp;
We consider the problem of determining when two delta-matroids on the same ground-set have a common base. Our approach is to adapt the theory of matchings in 2-polymatroids developed by Lovász \$[13]\$ to a new abstract system, which we call a parity system. Examples of parity systems may be obtained by combining either, two delta-matroids, or two orthogonal 2-polymatroids, on the same ground-sets. We show that many of the results of Lovász concerning 'double flowers' and 'projections' carry over to parity systems.
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